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Based on the authors’ lecture notes, **Introduction to the Theory of Statistical Inference** presents concise yet complete coverage of statistical inference theory, focusing on the fundamental classical principles. Suitable for a second-semester undergraduate course on statistical inference, the book offers proofs to support the mathematics. It illustrates core concepts using cartoons and provides solutions to all examples and problems.

**Highlights**

- Basic notations and ideas of statistical inference are explained in a mathematically rigorous, but understandable, form
- Classroom-tested and designed for students of mathematical statistics
- Examples, applications of the general theory to special cases, exercises, and figures provide a deeper insight into the material
- Solutions provided for problems formulated at the end of each chapter
- Combines the theoretical basis of statistical inference with a useful applied toolbox that includes linear models
- Theoretical, difficult, or frequently misunderstood problems are marked

The book is aimed at advanced undergraduate students, graduate students in mathematics and statistics, and theoretically-interested students from other disciplines. Results are presented as theorems and corollaries. All theorems are proven and important statements are formulated as guidelines in prose. With its multipronged and student-tested approach, this book is an excellent introduction to the theory of statistical inference.

Introduction

Statistical model

Data

Statistical Model

Statistic

Exponential Families

List of Problems

Further Reading

**Inference Principles**

Likelihood Function

Fisher Information

Sufficiency

List of Problems

Further Reading

**Estimation**

Methods of Estimation

Unbiasedness and Mean Squared Error

Asymptotic Properties of Estimators

List of Problems

Further Reading

**Testing Hypotheses**

Test problems

Tests: Assessing Evidence

Tests: Decision Rules

List of Problems

Further Reading

**Linear Model**

Introduction

Formulation of the Model

The Least Squares Estimator

The Normal Linear Model

List of Problems

Further Reading

**Solutions**

**Bibliography**

**Index**

Based on the authors’ lecture notes, **Introduction to the Theory of Statistical Inference** presents concise yet complete coverage of statistical inference theory, focusing on the fundamental classical principles. Suitable for a second-semester undergraduate course on statistical inference, the book offers proofs to support the mathematics. It illustrates core concepts using cartoons and provides solutions to all examples and problems.

**Highlights**

- Basic notations and ideas of statistical inference are explained in a mathematically rigorous, but understandable, form
- Classroom-tested and designed for students of mathematical statistics
- Examples, applications of the general theory to special cases, exercises, and figures provide a deeper insight into the material
- Solutions provided for problems formulated at the end of each chapter
- Combines the theoretical basis of statistical inference with a useful applied toolbox that includes linear models
- Theoretical, difficult, or frequently misunderstood problems are marked

The book is aimed at advanced undergraduate students, graduate students in mathematics and statistics, and theoretically-interested students from other disciplines. Results are presented as theorems and corollaries. All theorems are proven and important statements are formulated as guidelines in prose. With its multipronged and student-tested approach, this book is an excellent introduction to the theory of statistical inference.

Introduction

Statistical model

Data

Statistical Model

Statistic

Exponential Families

List of Problems

Further Reading

**Inference Principles**

Likelihood Function

Fisher Information

Sufficiency

List of Problems

Further Reading

**Estimation**

Methods of Estimation

Unbiasedness and Mean Squared Error

Asymptotic Properties of Estimators

List of Problems

Further Reading

**Testing Hypotheses**

Test problems

Tests: Assessing Evidence

Tests: Decision Rules

List of Problems

Further Reading

**Linear Model**

Introduction

Formulation of the Model

The Least Squares Estimator

The Normal Linear Model

List of Problems

Further Reading

**Solutions**

**Bibliography**

**Index**

Based on the authors’ lecture notes, **Introduction to the Theory of Statistical Inference** presents concise yet complete coverage of statistical inference theory, focusing on the fundamental classical principles. Suitable for a second-semester undergraduate course on statistical inference, the book offers proofs to support the mathematics. It illustrates core concepts using cartoons and provides solutions to all examples and problems.

**Highlights**

- Basic notations and ideas of statistical inference are explained in a mathematically rigorous, but understandable, form
- Classroom-tested and designed for students of mathematical statistics
- Examples, applications of the general theory to special cases, exercises, and figures provide a deeper insight into the material
- Solutions provided for problems formulated at the end of each chapter
- Combines the theoretical basis of statistical inference with a useful applied toolbox that includes linear models
- Theoretical, difficult, or frequently misunderstood problems are marked

The book is aimed at advanced undergraduate students, graduate students in mathematics and statistics, and theoretically-interested students from other disciplines. Results are presented as theorems and corollaries. All theorems are proven and important statements are formulated as guidelines in prose. With its multipronged and student-tested approach, this book is an excellent introduction to the theory of statistical inference.

Introduction

Statistical model

Data

Statistical Model

Statistic

Exponential Families

List of Problems

Further Reading

**Inference Principles**

Likelihood Function

Fisher Information

Sufficiency

List of Problems

Further Reading

**Estimation**

Methods of Estimation

Unbiasedness and Mean Squared Error

Asymptotic Properties of Estimators

List of Problems

Further Reading

**Testing Hypotheses**

Test problems

Tests: Assessing Evidence

Tests: Decision Rules

List of Problems

Further Reading

**Linear Model**

Introduction

Formulation of the Model

The Least Squares Estimator

The Normal Linear Model

List of Problems

Further Reading

**Solutions**

**Bibliography**

**Index**

**Introduction to the Theory of Statistical Inference** presents concise yet complete coverage of statistical inference theory, focusing on the fundamental classical principles. Suitable for a second-semester undergraduate course on statistical inference, the book offers proofs to support the mathematics. It illustrates core concepts using cartoons and provides solutions to all examples and problems.

**Highlights**

- Classroom-tested and designed for students of mathematical statistics
- Solutions provided for problems formulated at the end of each chapter
- Theoretical, difficult, or frequently misunderstood problems are marked

Introduction

Statistical model

Data

Statistical Model

Statistic

Exponential Families

List of Problems

Further Reading

**Inference Principles**

Likelihood Function

Fisher Information

Sufficiency

List of Problems

Further Reading

**Estimation**

Methods of Estimation

Unbiasedness and Mean Squared Error

Asymptotic Properties of Estimators

List of Problems

Further Reading

**Testing Hypotheses**

Test problems

Tests: Assessing Evidence

Tests: Decision Rules

List of Problems

Further Reading

**Linear Model**

Introduction

Formulation of the Model

The Least Squares Estimator

The Normal Linear Model

List of Problems

Further Reading

**Solutions**

**Bibliography**

**Index**

**Introduction to the Theory of Statistical Inference** presents concise yet complete coverage of statistical inference theory, focusing on the fundamental classical principles. Suitable for a second-semester undergraduate course on statistical inference, the book offers proofs to support the mathematics. It illustrates core concepts using cartoons and provides solutions to all examples and problems.

**Highlights**

- Classroom-tested and designed for students of mathematical statistics
- Solutions provided for problems formulated at the end of each chapter
- Theoretical, difficult, or frequently misunderstood problems are marked

Introduction

Statistical model

Data

Statistical Model

Statistic

Exponential Families

List of Problems

Further Reading

**Inference Principles**

Likelihood Function

Fisher Information

Sufficiency

List of Problems

Further Reading

**Estimation**

Methods of Estimation

Unbiasedness and Mean Squared Error

Asymptotic Properties of Estimators

List of Problems

Further Reading

**Testing Hypotheses**

Test problems

Tests: Assessing Evidence

Tests: Decision Rules

List of Problems

Further Reading

**Linear Model**

Introduction

Formulation of the Model

The Least Squares Estimator

The Normal Linear Model

List of Problems

Further Reading

**Solutions**

**Bibliography**

**Index**

**Introduction to the Theory of Statistical Inference** presents concise yet complete coverage of statistical inference theory, focusing on the fundamental classical principles. Suitable for a second-semester undergraduate course on statistical inference, the book offers proofs to support the mathematics. It illustrates core concepts using cartoons and provides solutions to all examples and problems.

**Highlights**

- Classroom-tested and designed for students of mathematical statistics
- Solutions provided for problems formulated at the end of each chapter
- Theoretical, difficult, or frequently misunderstood problems are marked

Introduction

Statistical model

Data

Statistical Model

Statistic

Exponential Families

List of Problems

Further Reading

**Inference Principles**

Likelihood Function

Fisher Information

Sufficiency

List of Problems

Further Reading

**Estimation**

Methods of Estimation

Unbiasedness and Mean Squared Error

Asymptotic Properties of Estimators

List of Problems

Further Reading

**Testing Hypotheses**

Test problems

Tests: Assessing Evidence

Tests: Decision Rules

List of Problems

Further Reading

**Linear Model**

Introduction

Formulation of the Model

The Least Squares Estimator

The Normal Linear Model

List of Problems

Further Reading

**Solutions**

**Bibliography**

**Index**